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<title>Simulations for Statistical and Thermal Physics</title>

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<h3 style="text-align:center;">Hard disks</h3>

<p class="header_title">Introduction</p>

<p>How can we understand the temperature and density
dependence of the equation of state and the structure of a dense
liquid? One way to gain more insight into this dependence is to modify the
interaction and see how the properties of the system change. In particular,
we would like to understand the relative role of the repulsive and attractive
parts of the interaction. Simulations of an idealized
system of hard disks (and hard spheres) have played an important role in the development of our understanding of simple liquids.</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;The interaction u(r) of two hard disks is given by</p>
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<img src="interaction.jpg" alt="" align="middle" >.
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<p>We see that u(r) is purely repulsive and that two hard disks cannot overlap.</p>


<p>&nbsp;&nbsp;&nbsp;&nbsp;We can simulate a system of hard disks by either solving the <a href="dynamics/index.html">equations of motion</a> or by using a <a href="metropolis/index.html">Monte Carlo algorithm</a>.</p>

<p class = "small">Updated 9 May 2008.</p>

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